Answer
The solution is $(4,5)$.
Work Step by Step
The given system of equations is
$8x-7y=-3$ ...... (1)
$6x-5y=-1$ ...... (2)
Multiply equation (1) by $-3$.
$\Rightarrow -3(8x-7y)=-3(-3)$
Use distributive property.
$\Rightarrow -24x+21y=9$ ...... (3)
Multiply equation (2) by $4$.
$\Rightarrow 4(6x-5y)=4(-1)$
Use distributive property.
$\Rightarrow 24x-20y=-4$ ...... (4)
Add equation (3) and (4).
$\Rightarrow -24x+21y+24x-20y=9-4$
Add like terms.
$\Rightarrow y=5$
Substitute $5$ for $y$ in equation (2).
$\Rightarrow 6x-5(5)=-1$
Simplify.
$\Rightarrow 6x-25=-1$
Add $25$ to each side.
$\Rightarrow 6x-25+25=-1+25$
Simplify.
$\Rightarrow 6x=24$
Divide each side by $6$.
$\Rightarrow \frac{6x}{6}=\frac{24}{6}$
Simplify.
$\Rightarrow x=4$
Check $(x,y)=(4,5)$
Equation (1):
$\Rightarrow 8x-7y=-3$
$\Rightarrow 8(4)-7(5)=-3$
$\Rightarrow 32-35=-3$
$\Rightarrow -3=-3$
True.
Equation (2):
$\Rightarrow 6x-5y=-1$
$\Rightarrow 6(4)-5(5)=-1$
$\Rightarrow 24-25=-1$
$\Rightarrow -1=-1$
True.
Hence, the solution is $(4,5)$.
